Electromagnetic form factors in the relativized Hypercentral CQM

M. De Sanctis, M.M.Giannini, E. Santopinto, A. Vassallo

Introduction

The hypercentral Constituent Quark Model

The elastic nucleon form factors (relativistic effects)

Conclusion

N05 Frascati, 13 october 2005

New Jlab data on nucleon f.f.

Give rise to problems:

• compatibility with old (Rosenbluth plot) data

• why the ratio GE/GM decreases?

• is there any zero in the f.f. ?

VMD models (fits)

FF = Fintr * VMD propagators

Mesons Fintr

JIL dipole

monopole

G K QCD-interpolation

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

Gari-Kruempelmann

Iachello

Skyrme Model

Holzwarth 1996,2002

ff given by soliton + VMD

dip at Q2 3 GeV2

Boosting of the solitondip at Q2 10 GeV2

Skyrmion (nucleon) mass 1648 MeV

The Hypercentral Constituent Quark Model

M. Ferraris et al., Phys. Lett. B364, 231 (1995)

PDG 4* & 3*

0.8

1

1.2

1.4

1.6

1.8

2

P11

P11'

P33

P33'

P11''

P31

F15P13

P33''F37

M

(GeV)

π=1π=1 π=−1

35F

13D11S

31S11S '15D33 13D D '

(70,1 -)

(56,0+)

(56,0+)'

(56,2+)(70,0+)

Jacobi coordinates

SPACE WAVE FUNCTION

1 2

3

= r - r1 2

√ 2

=r 2 rr1 + 2 - 3

√ 6

Hyperspherical coordinates

( (x

2 2+x = (size)

arc tg

(shape)

Quark-antiquark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)

3-quark lattice potential G.S. Bali Phys. Rep. 343, 1 (2001)

Electromagnetic properties

• Photocouplings M. Aiello et al., PL B387, 215 (1996)

• Helicity amplitudes (transition f.f.) M. Aiello et al., J. of Phys. G24, 753 (1998)

• Elastic form factors of the nucleon

M. De Sanctis et al., EPJ A1, 187 (1998)

• Structure functionsto be published

Fixed parameters predictions

Dynamical model (Mainz group)

please note

• the calculated proton radius is about 0.5 fm

(value previously obtained by fitting the helicity amplitudes)

• not good for elastic form factors

• there is lack of strength at low Q2 (outer region) in the e.m. transitions

• emerging picture: quark core (0.5 fm) plus (meson or sea-quark) cloud

ELASTIC FORM FACTORS

1. - Relativistic corrections to the elastic form factors

2. - Results with the semirelativistic CQM

3. - Quark form factors

1.- Relativistic corrections to form factors

• Breit frame• Lorentz boosts applied to the initial and final state• Expansion of current matrix elements up to first

order in quark momentum• Results

Arel (Q2) = F An.rel(Q2eff)

F = kin factor Q2eff = Q2 (MN/EN)2

De Sanctis et al. EPJ 1998

calculated

• 2.- Results with the semirelativistic CQM M. De Sanctis, M. G., E. Santopinto, A. Vassallo,

nucl-th/0506033

• Relativistic kinetic energy

• Boosts to initial and final states

• Expansion of current to any order

• Conserved current

and not much different from the NR case

V(x) = - /x + x

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Calculated values!

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Q2 F2p/F1

p

Q F2p/F1

p

3.- Quark form factors M. De Sanctis, M. G., E. Santopinto, A. Vassallo,

nucl-th/0506033

• Quark form factors are added in the current

ff = Fintr * quark form factors

semirelativistic hCQM input (calculated)

• Monopole + dipole form for qff

• Fit of:

– GEp/GM

p ratio (polarization data)

– GMp; GE

n ;GMn

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Q2 F2p/F1

p

Q F2p/F1

p

Conclusion

• The hCQM provides a consistent framework for the description of all the 4 nucleon electromagnetic form factors

• Relativity is crucial in explaining the decrease of the ratio GE/GM

• Quark form factors are necessary in order to get a good reproduction of the Q2 behaviour (meson cloud is missing)